Ch4 First Half - Vertex/Standard/Intercept Factoring GOOD

Front

What is the range of a quadratic function in vertex form?

Back

The range of a quadratic function in vertex form is determined by the vertex's y-coordinate. If the vertex is (h, k) and opens upwards, the range is y ≥ k. If it opens downwards, the range is y ≤ k.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a quadratic function given in standard form?

Back

To find the vertex of a quadratic function in standard form (ax² + bx + c), use the formula h = -b/(2a) and then substitute h back into the function to find k.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form (y = a(x - h)² + k) to standard form (ax² + bx + c), expand the equation and simplify.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value in a quadratic equation determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, also known as the solutions of the equation.

Front

How can you find the roots of a quadratic equation using factoring?

Back

To find the roots of a quadratic equation using factoring, express the equation in the form (x - r1)(x - r2) = 0, where r1 and r2 are the roots.

Front

What is the intercept form of a quadratic equation?

Back

The intercept form of a quadratic equation is y = a(x - p)(x - q), where p and q are the x-intercepts of the parabola.